Finite Presentation of Alternating Groups

Graham Higman posed the question: How small can the integers p and q be made, while maintaining the property that all but finitly many alternating and symmetric groups are factor groups of .(2,p,q) = (x, y : x² = y. = (xy). = 1)? He proved that for a sufficiently large == n, the alternating group is a homomorphic image of the triangle group .(2,p,q) where p = 3 and q=7. Later, his result was generalized by proving the result for p 3 and q.7. Choosing = P=4 and q.17 in this paper we have answered the "Hiqman Question".